1. Field of the Invention
The invention relates to a method of localizing an object in a turbid medium, which method includes the following steps:
irradiating the turbid medium and determining an intensity of a part of the light transported through the turbid medium along a plurality of light paths, from source points at which the light enters the turbid medium, to detector points at which the light leaves the turbid medium determining an estimated intensity of the light of a selected light path by way of a first combination of predetermined attenuation coefficients of voxels of the turbid medium and a predetermined weighting function which is related to a position of a voxel relative to the selected light path, PA0 determining a difference between an estimated intensity and the determined intensity for the selected light path, and determining a next value of the attenuation coefficients of the voxels by way of a second combination of the differences determined for the plurality of light paths. PA0 selecting a first axis of an orthogonal system which corresponds best to the direction of the selected light path, approximating the selected light path in the turbid medium by light path voxels, PA0 determining a plane perpendicular to the selected light path, said perpendicular plane being determined by a light path voxel and the first and the second orthogonal vector, PA0 approximating a first auxiliary line in the perpendicular plane which is oriented substantially parallel to the first orthogonal vector through first voxels, PA0 determining a table of a function W(s), dependent on the first vector, whose elements contain contributions of W(s) which are dependent on the distance between a first voxel and the selected light path, PA0 determining a partial sum of the estimated intensity of contributions by various first voxels as a product of a function W(t) which is dependent on the second orthogonal vector and elements of W(s). The first axis is chosen in such a manner that, relative to the two other axes of the orthogonal system, it is situated nearest to the selected light path. The number of calculations of an exponential function can thus be reduced by precalculation of W(t) along the first auxiliary line. The contribution to the estimated intensity of a selected light path for a plurality of voxels contained in the normal plane is subsequently determined, for example as the product of W(s) and an interpolated value of W(t). The interpolated value of W(t) is determined, for example by a zero-order or first-order interpolation. The contribution of substantially all voxels of the perpendicular plane to the estimated intensity of the selected light path can be determined by repeating this step, without it being necessary to calculate an exponential function for each voxel. In order to determine the estimated intensity associated with the selected light path, the contributions of substantially all voxels in the turbid medium is determined by successively determining the partial sums of the voxels of successive perpendicular planes which are situated along the selected light path and contain respective, successive light path voxels. PA0 and a processing unit for reconstructing an image of the interior of the turbid medium on the basis of the measured intensities, the processing unit also including means for determining an estimated intensity of the light near a detecter point of a light path by means of a first combination of predetermined attenuation coefficients of voxels of the turbid medium and a predetermined weighting function which is dependent on a position of the voxel relative to the selected light path, PA0 means for determining a difference between the estimated intensity and the measured intensity, and PA0 means for determining a next value of the attenuation coefficient of a voxel by means of a second combination of the differences determined for the plurality of light paths. It is further object of the invention to provide a device for the imaging of object in a turbid medium which device reduces the calculation time for reconstruction of images. To this end the device according to the invention is characterized in that the weighting function contains a function which can be factorized to a first and a second orthogonal vector which extend transversely of the selected light path.
The invention also relates to a device for carrying out a method of this kind.
2. Description of the Related Art
In the context of the present application the term light is to be understood to mean electromagnetic radiation of a wavelength in the range of from 400 to 1400 nm. Furthermore, a turbid medium is to be understood to mean a substance consisting of a material having a high light scattering coefficient. Examples in this respect are an Intralipid solution or biological tissue. Furthermore, an attenuation coefficient is to be understood to mean the inverse diffuse absorption distance .kappa..
A method of this kind is known from the article "The forward and inverse problems in time resolved infra-red imaging", by S. R. Arridge, as published in Medical Optical Tomography, No. IS11, 1993, pp. 35-64. The known iterative method of imaging the interior of the turbid medium is based on a three-dimensional set of attenuation coefficients .kappa. which correspond to the voxels of the turbid medium. Subsequently, for the respective light paths the estimated intensity is determined as the sum of the contributions of the change in intensity due to the predetermined attenuation coefficient of the voxels of the turbid medium. Subsequently, a difference set is determined from the estimated intensities and the measured intensities. Using the second combinations of the values of the difference set, corrections are determined for the attenuation coefficients .kappa. of the three-dimensional set.
After several iterations, the values of the attenuation coefficients .kappa. have converged and the values of the attenuation coefficient which correspond to different voxels in a plane can be represented in an image. The change of the estimated intensity dI of a selected light path due to a change .DELTA..kappa. of the attenuation coefficient .kappa. of a volume element V is given by the formule: ##EQU1## in which .vertline.sd.vertline. is the length of the selected light path, .vertline.sp.vertline. is the distance between a measuring light source and the voxel, and .vertline.pd.vertline. is the distance between the voxel and a photodetector opening. The formule (1) can subsequently be approximated by a product of a first function W(x.sub.s,K) and the weighting function W(x.sub.S,.rho.,K), where K equals the product of the attenuation coefficient .kappa. and the selected light path .vertline.sd.vertline. which is equal to the distance between the measuring light source and a photodetector opening. Furthermore, .kappa. is determined by .kappa.=.sqroot.3.mu..mu..sub.a .mu..sub.s in which .mu..sub.a represents the absorption coefficient and .mu..sub.s ' is the transport coefficient or the reduced scatter coefficient. The function W(x.sub.s,K) is determined by ##EQU2## In the diffusion approximation for infinite media, the weighting function W(x.sub.s,.rho., K) can be approximated by the formule ##EQU3## in which x.sub.s is the distance between the light source and the shortest connecting line between the voxel and the selected light path and .rho. is the distance between the voxel and the selected light path, both said distances being normalized to the length of the selected shortest light path.
It is a drawback of the known method that the last formule (3) contains an exponential function and must be calculated separately for each voxel and for each light path through the turbid medium; these operations are comparatively time-consuming.